Generalized Z-Solitons with Some Connections

This paper presents a broader formulation of Ricci solitons through the introduction of a generalized class of Z-solitons on Riemannian manifolds that admit either semi-symmetric metric or semi-symmetric non-metric affine connections. The study primarily concentrates on the differential geometric properties of these solitons, with particular attention given to scenarios where the associated vector field exhibits torse-forming behavior in accordance with the geometry induced by the semi-symmetric connection.